Collection Of theses on high power laser and plasma physics, Volume. 10, Issue 1, 358(2010)
Fractional Fourier transform of flat-topped multi-Gaussian beams
[1] [1] V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980)
[2] [2] J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Programmable two-dimensional optical fractional Fourier processor,” Opt. Express 17, 4976–4983 (2009)
[3] [3] H. M. Ozaktas and D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995)
[4] [4] H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators,” Opt. Lett. 19, 1678–1680 (1994)
[5] [5] P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994)
[6] [6] G. Q. Zhou, “Fractional Fourier transform of Lorentz–Gauss beams,” J. Opt. Soc. Am. A 26, 350–355 (2009)
[7] [7] F. Wang and Y. J. Cai, “Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics,” J. Opt. Soc. Am. A 24, 1937–1944 (2007)
[8] [8] Z. J. Liu and S. T. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007)
[9] [9] Q. Gao, T. H. Liao, and Y. F. Cui, “Solving the phaseretrieval problem of a complex signal in the fractional Fourier domain by nonlinear least-squares,” Opt. Lett. 33, 1899–1901 (2008)
[10] [10] D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993)
[11] [11] H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993)
[12] [12] D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform,” Appl. Opt. 33, 6188–6193 (1994)
[13] [13] A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993)
[14] [14] S. D. Silvestri, P. Laporta, V. Magni, O. Svelto, and B. Majocchi, “Unstable laser resonators with super-Gaussian mirrors,” Opt. Lett. 13, 201–203 (1988)
[15] [15] J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988)
[16] [16] F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994)
[17] [17] Y. Li, “Light beams with flat-topped profiles,” Opt. Lett. 27, 1007–1009 (2002)
[18] [18] A. A. Tovar, “Propagation of flat-topped multi-Gaussian laser beams,” J. Opt. Soc. Am. A 18, 1897–1904 (2001)
[19] [19] Y. Q Gao, B. Q. Zhu, D. Z. Liu, and Z. Q. Lin, “Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures,” Opt. Express 17, 12753–12766 (2009)
[20] [20] Y. Q. Gao, B. Q. Zhu, D. Z. Liu, and Z. Q. Lin, “Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system,” J. Opt. Soc. Am. A 26, 2139–2146 (2009)
[21] [21] M. A. Bandres and J. C. Gutierrez-Vaga, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express 15, 16719–16727 (2007)
[22] [22] G. Q. Zhou, “Fractional Fourier transform of a higher-order cosh-Gaussian beam,” J. Mod. Opt. 2009. 56, 886–892 (2009)
[23] [23] B.Tang and M. H. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276–1282 (2009)
[24] [24] J. N. McMullin, “The ABCD matrix in arbitrarily tapered quadratic-index waveguides,” Appl. Opt. 25, 2184–2187 (1986)
[25] [25] S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970)
[26] [26] J. N. Chen, “Propagation and transformation of flat-topped multi-Gaussian beams in a general nonsymmetrical apertured double-lens system,” J. Opt. Soc. Am. A 24, 84–92 (2007)
[27] [27] H. Mao and D. Zhao, “Different models for a hard-aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system,” J. Opt. Soc. Am. A 22, 647–653 (2005).
Get Citation
Copy Citation Text
Yan-Qi Gao, Bao-Qiang Zhu, Dai-Zhong Liu, Zun-Qi Lin. Fractional Fourier transform of flat-topped multi-Gaussian beams[J]. Collection Of theses on high power laser and plasma physics, 2010, 10(1): 358